Graph Transplant: Node Saliency-Guided Graph mixup with Local Structure Preservation

1. Graph Transplant: Node Saliency-Guided
Graph Mixup with Local Structure
Preservation
Joonhyung Park ∗, Hajin Shim ∗, Eunho Yang
AAAI 2022
Machine Learning & Intelligence Laboratory
∗
: Equal Contribution

2. • Generating virtual augmented data via interpolation of two images
Mixup-based Augmentation
Image 𝐗𝐀
Image 𝐗𝐁
CutMix (ICCV’19)
Mixup (ICLR’18)
𝑌
𝐴 (Fish)
0.5
𝑌𝐵 (Bird)
0.5
0.85
0.15
𝑌
𝐴 (Fish) 𝑌𝐵 (Bird)

3. • Advantages of Mixup-based augmentations
• Improve generalization performance (smooth decision boundary) 1
• Refine model calibration and predictive uncertainty of neural networks 2
• Enhance model robustness to data corruption 3
Mixup-based Augmentation
1) Manifold Mixup: Better Representations by Interpolating Hidden States, ICML’19
2) On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks, NeurIPS’19
3) AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty, ICLR’20

4. • Non-trivial challenges for Graph Mixup
• No node correspondence
• The number of nodes may differ across graph instances
• Irregular connectivity
How about Graph-structured Data?
We propose the first Mixup-like graph augmentation method Graph Transplant
Graph 𝑮𝝅 Graph 𝑮
How to interpolate two dissimilar-structured graphs?

5. • 𝒌-hop subgraph is defined as a mixing unit that can preserve the local information
• Graph Transplant employs the node saliency information to select meaningful
subgraphs
• Node saliency encodes the importance of each node in classifying graph property
Graph Transplant: Salient Subgraph Extraction
Saliency of node 𝒗
Salient nodes

6. • 𝒌-hop subgraph is defined as a mixing unit that can preserve the local information
• Graph Transplant employs the node saliency information to select meaningful
subgraphs
• Salient subgraph is extracted in to be attached with another random subgraph
• Salient subgraph: 𝑘-hop subgraph anchored by salient nodes
Graph Transplant: Salient Subgraph Extraction
Graph 𝐺𝜋
Graph 𝐺
Salient Subgraph of 𝐺𝜋
Random Subgraph of 𝐺𝜋
: Anchor nodes

7. Graph Transplant: Connecting Two Subgraphs
• After extracting subgraphs, subgraphs are transplanted by adding new edges
• We propose two approaches for determining the connectivity of subgraphs
• DP (Degree Preservation): Random connection under the constraint on the original node
degree (preserves the expected degree of the nodes in the original graphs)
• EP (Edge Prediction): Predict edge probability by using a differentiable edge predictor
based on node features
Concept of Edge Prediction

8. Graph Transplant: Adaptive Label Mixing
• Assigning the appropriate label to the generated graph is necessary to prevent the
network from being misled by inappropriate supervision
• Simply assigning the label in proportion to the number of nodes will NOT explain the
generated graph properly
• Our label mixing strategy determines the label for mixed graph as the ratio of the
saliency between subgraphs
• The label ℓ for the mixed graph 𝐺′
is defined as:
∗ ℐ 𝑆 , ഥ
𝑉 =
σ𝑣∈𝑉 𝑠𝑣
𝑆
(Importance function; total saliency ratio of the nodes constituting the subgraph in the full graph)
ℓ 𝑦𝐺𝜋
, 𝑦𝐺 = 𝜆𝐺′𝑦𝐺𝜋
+ 1 − 𝜆𝐺′ 𝑦𝐺
𝜆𝐺′ =
ℐ(𝑆𝐺𝜋
, ഥ
𝑉
𝜋 )
ℐ 𝑆𝐺𝜋
, ഥ
𝑉
𝜋 + ℐ(𝑆𝐺 , 𝑉ത
𝑉)
Importance of Subgraph derived from 𝐺𝜋
Importance of Subgraph derived from 𝐺

9. • Graph Transplant consistently achieves the best performances for 5 graph classification
benchmark datasets
• Graph Transplant consistently exhibits superiority for datasets with different
characteristics such as sparsity of connection, graph size, and the presence or absence
of node features
Graph Classification Results

10. • We test if the GNNs trained with Graph Transplant can enhance the model robustness
against adversarial attacks.
• GradArgmax (Dai et al. 2018): Gradient based white-box attack designed for graph-
structured data
• Interestingly, although the adversarial attack is based on edge modification, ours
exhibits better performance than PermE, an edge perturbation augmentation.
Robustness to Adversarial Attack

11. • We analyze the node saliency of the molecular graphs to show that our method leads
the model to attend where it really matters to correctly classify molecules
• The task is to decide whether the molecule causes DNA mutation or not, which is
important to capture the interaction of functional groups
• E.g. The left case in Figure is of a mutagenic molecule in that it has two methyl groups attached to oxygen atoms,
which are vulnerable to radical attack. Attacked by radical, the attached methyl groups are transferred to DNA
base, entailing the change of DNA property, resulting in mutation. While the model trained with Graph
Transplant attends to the appropriate region, the vanilla model gives an incorrect answer with highlighting the
unrelated spot
Qualitative Analysis

12. • We proposed Graph Transplant, the first input-level Mixup strategy for graph data, that
generates mixed graphs via the guidance of the node saliency
• Our contribution
• We propose Graph Transplant, that can mix two dissimilar-structured graphs by replacing the
destination subgraph with the source subgraph while preserving the local structure
• In contrast to random augmentations, we present a novel strategy to generate properly mixed
graphs with adaptively assigned labels that adheres to the corresponding labels by explicitly
leveraging the node saliency
• Through extensive experiments, we show that Graph Transplant is an effective algorithm that
can bring overall improvement across the multiple fields of graphs in terms of the
classification performance, robustness, and model calibration.
Conclusion